regressionAnalysisWithPython/03/Chapter3_Multiple_Regression_Analysis.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter3 Multiple Regression analysis\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 초기 개발환경 세팅을 위한 준비 및 데이터 불러오기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn import linear_model\n",
    "%matplotlib inline\n",
    "boston = load_boston()\n",
    "dataset = pd.DataFrame(boston.data, columns=boston.feature_names) # 데이터 Frame화는 필수!!! 첫번째 각각의 새로줄에  columns에 기능 이름들을 였자\n",
    "dataset['target'] = boston.target\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "공공 데이터인 sklearn.dataset중에서 load_boston을 불러오자!!!  \n",
    "`from sklearn.datasets import load_boston`  패키지를 불러올 때 모듈 전체를 가져오는게 아니라 변수만 가져오려고 하는 것이다!  \n",
    "밑에 dataFrame의 예제를 통해 모듈사용 법을 익혀보자!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "   48  49  50\n2   1   2   3\nA   4   5   6\n4   7   8   9",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>48</th>\n      <th>49</th>\n      <th>50</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>2</th>\n      <td>1</td>\n      <td>2</td>\n      <td>3</td>\n    </tr>\n    <tr>\n      <th>A</th>\n      <td>4</td>\n      <td>5</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>7</td>\n      <td>8</td>\n      <td>9</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {}
    }
   ],
   "source": [
    "df = pd.DataFrame(data=np.array([[1,2,3],[4,5,6],[7,8,9]]),index=[2, 'A', 4], columns=[48,49,50])\n",
    "display(df)  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "observations = len(dataset) # dataset 길이 측정\n",
    "variables = dataset.columns[:-1] # 세로줄 항목 단어들 불러옴\n",
    "X = dataset.iloc[:,:-1] # iloc : 값보기 -1 하는 이유 마지막 y값 타겟을 빼기 위해\n",
    "y = dataset['target'].values    # target value를 불러와보자"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이제 X와 y값에 뭐가 저장되어있는지 보자"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "        CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n0    0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n1    0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n2    0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n3    0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n4    0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n..       ...   ...    ...   ...    ...    ...   ...     ...  ...    ...   \n501  0.06263   0.0  11.93   0.0  0.573  6.593  69.1  2.4786  1.0  273.0   \n502  0.04527   0.0  11.93   0.0  0.573  6.120  76.7  2.2875  1.0  273.0   \n503  0.06076   0.0  11.93   0.0  0.573  6.976  91.0  2.1675  1.0  273.0   \n504  0.10959   0.0  11.93   0.0  0.573  6.794  89.3  2.3889  1.0  273.0   \n505  0.04741   0.0  11.93   0.0  0.573  6.030  80.8  2.5050  1.0  273.0   \n\n     PTRATIO       B  LSTAT  \n0       15.3  396.90   4.98  \n1       17.8  396.90   9.14  \n2       17.8  392.83   4.03  \n3       18.7  394.63   2.94  \n4       18.7  396.90   5.33  \n..       ...     ...    ...  \n501     21.0  391.99   9.67  \n502     21.0  396.90   9.08  \n503     21.0  396.90   5.64  \n504     21.0  393.45   6.48  \n505     21.0  396.90   7.88  \n\n[506 rows x 13 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>CRIM</th>\n      <th>ZN</th>\n      <th>INDUS</th>\n      <th>CHAS</th>\n      <th>NOX</th>\n      <th>RM</th>\n      <th>AGE</th>\n      <th>DIS</th>\n      <th>RAD</th>\n      <th>TAX</th>\n      <th>PTRATIO</th>\n      <th>B</th>\n      <th>LSTAT</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.00632</td>\n      <td>18.0</td>\n      <td>2.31</td>\n      <td>0.0</td>\n      <td>0.538</td>\n      <td>6.575</td>\n      <td>65.2</td>\n      <td>4.0900</td>\n      <td>1.0</td>\n      <td>296.0</td>\n      <td>15.3</td>\n      <td>396.90</td>\n      <td>4.98</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.02731</td>\n      <td>0.0</td>\n      <td>7.07</td>\n      <td>0.0</td>\n      <td>0.469</td>\n      <td>6.421</td>\n      <td>78.9</td>\n      <td>4.9671</td>\n      <td>2.0</td>\n      <td>242.0</td>\n      <td>17.8</td>\n      <td>396.90</td>\n      <td>9.14</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.02729</td>\n      <td>0.0</td>\n      <td>7.07</td>\n      <td>0.0</td>\n      <td>0.469</td>\n      <td>7.185</td>\n      <td>61.1</td>\n      <td>4.9671</td>\n      <td>2.0</td>\n      <td>242.0</td>\n      <td>17.8</td>\n      <td>392.83</td>\n      <td>4.03</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.03237</td>\n      <td>0.0</td>\n      <td>2.18</td>\n      <td>0.0</td>\n      <td>0.458</td>\n      <td>6.998</td>\n      <td>45.8</td>\n      <td>6.0622</td>\n      <td>3.0</td>\n      <td>222.0</td>\n      <td>18.7</td>\n      <td>394.63</td>\n      <td>2.94</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.06905</td>\n      <td>0.0</td>\n      <td>2.18</td>\n      <td>0.0</td>\n      <td>0.458</td>\n      <td>7.147</td>\n      <td>54.2</td>\n      <td>6.0622</td>\n      <td>3.0</td>\n      <td>222.0</td>\n      <td>18.7</td>\n      <td>396.90</td>\n      <td>5.33</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>501</th>\n      <td>0.06263</td>\n      <td>0.0</td>\n      <td>11.93</td>\n      <td>0.0</td>\n      <td>0.573</td>\n      <td>6.593</td>\n      <td>69.1</td>\n      <td>2.4786</td>\n      <td>1.0</td>\n      <td>273.0</td>\n      <td>21.0</td>\n      <td>391.99</td>\n      <td>9.67</td>\n    </tr>\n    <tr>\n      <th>502</th>\n      <td>0.04527</td>\n      <td>0.0</td>\n      <td>11.93</td>\n      <td>0.0</td>\n      <td>0.573</td>\n      <td>6.120</td>\n      <td>76.7</td>\n      <td>2.2875</td>\n      <td>1.0</td>\n      <td>273.0</td>\n      <td>21.0</td>\n      <td>396.90</td>\n      <td>9.08</td>\n    </tr>\n    <tr>\n      <th>503</th>\n      <td>0.06076</td>\n      <td>0.0</td>\n      <td>11.93</td>\n      <td>0.0</td>\n      <td>0.573</td>\n      <td>6.976</td>\n      <td>91.0</td>\n      <td>2.1675</td>\n      <td>1.0</td>\n      <td>273.0</td>\n      <td>21.0</td>\n      <td>396.90</td>\n      <td>5.64</td>\n    </tr>\n    <tr>\n      <th>504</th>\n      <td>0.10959</td>\n      <td>0.0</td>\n      <td>11.93</td>\n      <td>0.0</td>\n      <td>0.573</td>\n      <td>6.794</td>\n      <td>89.3</td>\n      <td>2.3889</td>\n      <td>1.0</td>\n      <td>273.0</td>\n      <td>21.0</td>\n      <td>393.45</td>\n      <td>6.48</td>\n    </tr>\n    <tr>\n      <th>505</th>\n      <td>0.04741</td>\n      <td>0.0</td>\n      <td>11.93</td>\n      <td>0.0</td>\n      <td>0.573</td>\n      <td>6.030</td>\n      <td>80.8</td>\n      <td>2.5050</td>\n      <td>1.0</td>\n      <td>273.0</td>\n      <td>21.0</td>\n      <td>396.90</td>\n      <td>7.88</td>\n    </tr>\n  </tbody>\n</table>\n<p>506 rows × 13 columns</p>\n</div>"
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      "text/plain": "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n       18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n       15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n       13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n       21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n       35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n       19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n       20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n       23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n       33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n       21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n       20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n       23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n       15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n       17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n       25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n       23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n       32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n       34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n       20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n       26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n       31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n       22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n       42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n       36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n       32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n       20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n       20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n       22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n       21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n       19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n       32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n       18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n       16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n       13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n        7.2, 10.5,  7.4, 10.2, 11.5, 15.1, 23.2,  9.7, 13.8, 12.7, 13.1,\n       12.5,  8.5,  5. ,  6.3,  5.6,  7.2, 12.1,  8.3,  8.5,  5. , 11.9,\n       27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n        8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n        9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n       10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n       15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n       19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n       29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n       20.6, 21.2, 19.1, 20.6, 15.2,  7. ,  8.1, 13.6, 20.1, 21.8, 24.5,\n       23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9])"
     },
     "metadata": {}
    }
   ],
   "source": [
    "display(X)\n",
    "display(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "X값에는 각 항목별로 특징들이 나타나고\n",
    "y값에는 X값을 구할때 뺀 마지막 column 값들이 저장되어있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ix -> iloc  \n",
    " [[:,:]] -> row, column 둘다 전부 불러오겠다.  \n",
    " [[:,:-1]] -> row, column -1 을 전부 불러오겠다.(target값을 빼기 위해) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using multiple features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm            \n",
    "import statsmodels.formula.api as smf\n",
    "Xc = sm.add_constant(X)   # X데이타를 api에 였자\n",
    "linear_regression = sm.OLS(y,Xc)\n",
    "fitted_model = linear_regression.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "앞에서 Statsmodels를 사용한 것처럼 패키지에서 필요한 모듈을 다시 로드(하나는 행렬로, 다른 하나는 수식으로 작업)  \n",
    "api 사용하니 이마이 편하다....  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:                      y   R-squared:                       0.741\nModel:                            OLS   Adj. R-squared:                  0.734\nMethod:                 Least Squares   F-statistic:                     108.1\nDate:                Thu, 13 Aug 2020   Prob (F-statistic):          6.72e-135\nTime:                        15:10:05   Log-Likelihood:                -1498.8\nNo. Observations:                 506   AIC:                             3026.\nDf Residuals:                     492   BIC:                             3085.\nDf Model:                          13                                         \nCovariance Type:            nonrobust                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------\nconst         36.4595      5.103      7.144      0.000      26.432      46.487\nCRIM          -0.1080      0.033     -3.287      0.001      -0.173      -0.043\nZN             0.0464      0.014      3.382      0.001       0.019       0.073\nINDUS          0.0206      0.061      0.334      0.738      -0.100       0.141\nCHAS           2.6867      0.862      3.118      0.002       0.994       4.380\nNOX          -17.7666      3.820     -4.651      0.000     -25.272     -10.262\nRM             3.8099      0.418      9.116      0.000       2.989       4.631\nAGE            0.0007      0.013      0.052      0.958      -0.025       0.027\nDIS           -1.4756      0.199     -7.398      0.000      -1.867      -1.084\nRAD            0.3060      0.066      4.613      0.000       0.176       0.436\nTAX           -0.0123      0.004     -3.280      0.001      -0.020      -0.005\nPTRATIO       -0.9527      0.131     -7.283      0.000      -1.210      -0.696\nB              0.0093      0.003      3.467      0.001       0.004       0.015\nLSTAT         -0.5248      0.051    -10.347      0.000      -0.624      -0.425\n==============================================================================\nOmnibus:                      178.041   Durbin-Watson:                   1.078\nProb(Omnibus):                  0.000   Jarque-Bera (JB):              783.126\nSkew:                           1.521   Prob(JB):                    8.84e-171\nKurtosis:                       8.281   Cond. No.                     1.51e+04\n==============================================================================\n\nWarnings:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n[2] The condition number is large, 1.51e+04. This might indicate that there are\nstrong multicollinearity or other numerical problems.\n\"\"\"",
      "text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.741</td> \n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.734</td> \n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   108.1</td> \n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 13 Aug 2020</td> <th>  Prob (F-statistic):</th> <td>6.72e-135</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>15:10:05</td>     <th>  Log-Likelihood:    </th> <td> -1498.8</td> \n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3026.</td> \n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>   492</td>      <th>  BIC:               </th> <td>   3085.</td> \n</tr>\n<tr>\n  <th>Df Model:</th>              <td>    13</td>      <th>                     </th>     <td> </td>    \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>const</th>   <td>   36.4595</td> <td>    5.103</td> <td>    7.144</td> <td> 0.000</td> <td>   26.432</td> <td>   46.487</td>\n</tr>\n<tr>\n  <th>CRIM</th>    <td>   -0.1080</td> <td>    0.033</td> <td>   -3.287</td> <td> 0.001</td> <td>   -0.173</td> <td>   -0.043</td>\n</tr>\n<tr>\n  <th>ZN</th>      <td>    0.0464</td> <td>    0.014</td> <td>    3.382</td> <td> 0.001</td> <td>    0.019</td> <td>    0.073</td>\n</tr>\n<tr>\n  <th>INDUS</th>   <td>    0.0206</td> <td>    0.061</td> <td>    0.334</td> <td> 0.738</td> <td>   -0.100</td> <td>    0.141</td>\n</tr>\n<tr>\n  <th>CHAS</th>    <td>    2.6867</td> <td>    0.862</td> <td>    3.118</td> <td> 0.002</td> <td>    0.994</td> <td>    4.380</td>\n</tr>\n<tr>\n  <th>NOX</th>     <td>  -17.7666</td> <td>    3.820</td> <td>   -4.651</td> <td> 0.000</td> <td>  -25.272</td> <td>  -10.262</td>\n</tr>\n<tr>\n  <th>RM</th>      <td>    3.8099</td> <td>    0.418</td> <td>    9.116</td> <td> 0.000</td> <td>    2.989</td> <td>    4.631</td>\n</tr>\n<tr>\n  <th>AGE</th>     <td>    0.0007</td> <td>    0.013</td> <td>    0.052</td> <td> 0.958</td> <td>   -0.025</td> <td>    0.027</td>\n</tr>\n<tr>\n  <th>DIS</th>     <td>   -1.4756</td> <td>    0.199</td> <td>   -7.398</td> <td> 0.000</td> <td>   -1.867</td> <td>   -1.084</td>\n</tr>\n<tr>\n  <th>RAD</th>     <td>    0.3060</td> <td>    0.066</td> <td>    4.613</td> <td> 0.000</td> <td>    0.176</td> <td>    0.436</td>\n</tr>\n<tr>\n  <th>TAX</th>     <td>   -0.0123</td> <td>    0.004</td> <td>   -3.280</td> <td> 0.001</td> <td>   -0.020</td> <td>   -0.005</td>\n</tr>\n<tr>\n  <th>PTRATIO</th> <td>   -0.9527</td> <td>    0.131</td> <td>   -7.283</td> <td> 0.000</td> <td>   -1.210</td> <td>   -0.696</td>\n</tr>\n<tr>\n  <th>B</th>       <td>    0.0093</td> <td>    0.003</td> <td>    3.467</td> <td> 0.001</td> <td>    0.004</td> <td>    0.015</td>\n</tr>\n<tr>\n  <th>LSTAT</th>   <td>   -0.5248</td> <td>    0.051</td> <td>  -10.347</td> <td> 0.000</td> <td>   -0.624</td> <td>   -0.425</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>178.041</td> <th>  Durbin-Watson:     </th> <td>   1.078</td> \n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 783.126</td> \n</tr>\n<tr>\n  <th>Skew:</th>          <td> 1.521</td>  <th>  Prob(JB):          </th> <td>8.84e-171</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 8.281</td>  <th>  Cond. No.          </th> <td>1.51e+04</td> \n</tr>\n</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.51e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "fitted_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "여기서 R-squared와 Adj R-squared를 살펴 보아야한다.   \n",
    "**R-squared** : 회귀선이 얼마나 적합하게 모델링이 되어 있는지를 유추해서 볼수 있게한다.  \n",
    "　  \n",
    "R-square : $$ R^2=\\frac{SSR}{SST} = 1 - \\frac{SSE}{SST}$$이다.  \n",
    "여기서 `SSE`는 `Sum of Square Error`로 회귀식과 실제값의 차이를 의미한다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "             CRIM        ZN     INDUS      CHAS       NOX        RM       AGE  \\\nCRIM     1.000000 -0.200469  0.406583 -0.055892  0.420972 -0.219247  0.352734   \nZN      -0.200469  1.000000 -0.533828 -0.042697 -0.516604  0.311991 -0.569537   \nINDUS    0.406583 -0.533828  1.000000  0.062938  0.763651 -0.391676  0.644779   \nCHAS    -0.055892 -0.042697  0.062938  1.000000  0.091203  0.091251  0.086518   \nNOX      0.420972 -0.516604  0.763651  0.091203  1.000000 -0.302188  0.731470   \nRM      -0.219247  0.311991 -0.391676  0.091251 -0.302188  1.000000 -0.240265   \nAGE      0.352734 -0.569537  0.644779  0.086518  0.731470 -0.240265  1.000000   \nDIS     -0.379670  0.664408 -0.708027 -0.099176 -0.769230  0.205246 -0.747881   \nRAD      0.625505 -0.311948  0.595129 -0.007368  0.611441 -0.209847  0.456022   \nTAX      0.582764 -0.314563  0.720760 -0.035587  0.668023 -0.292048  0.506456   \nPTRATIO  0.289946 -0.391679  0.383248 -0.121515  0.188933 -0.355501  0.261515   \nB       -0.385064  0.175520 -0.356977  0.048788 -0.380051  0.128069 -0.273534   \nLSTAT    0.455621 -0.412995  0.603800 -0.053929  0.590879 -0.613808  0.602339   \n\n              DIS       RAD       TAX   PTRATIO         B     LSTAT  \nCRIM    -0.379670  0.625505  0.582764  0.289946 -0.385064  0.455621  \nZN       0.664408 -0.311948 -0.314563 -0.391679  0.175520 -0.412995  \nINDUS   -0.708027  0.595129  0.720760  0.383248 -0.356977  0.603800  \nCHAS    -0.099176 -0.007368 -0.035587 -0.121515  0.048788 -0.053929  \nNOX     -0.769230  0.611441  0.668023  0.188933 -0.380051  0.590879  \nRM       0.205246 -0.209847 -0.292048 -0.355501  0.128069 -0.613808  \nAGE     -0.747881  0.456022  0.506456  0.261515 -0.273534  0.602339  \nDIS      1.000000 -0.494588 -0.534432 -0.232471  0.291512 -0.496996  \nRAD     -0.494588  1.000000  0.910228  0.464741 -0.444413  0.488676  \nTAX     -0.534432  0.910228  1.000000  0.460853 -0.441808  0.543993  \nPTRATIO -0.232471  0.464741  0.460853  1.000000 -0.177383  0.374044  \nB        0.291512 -0.444413 -0.441808 -0.177383  1.000000 -0.366087  \nLSTAT   -0.496996  0.488676  0.543993  0.374044 -0.366087  1.000000  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>CRIM</th>\n      <th>ZN</th>\n      <th>INDUS</th>\n      <th>CHAS</th>\n      <th>NOX</th>\n      <th>RM</th>\n      <th>AGE</th>\n      <th>DIS</th>\n      <th>RAD</th>\n      <th>TAX</th>\n      <th>PTRATIO</th>\n      <th>B</th>\n      <th>LSTAT</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>CRIM</th>\n      <td>1.000000</td>\n      <td>-0.200469</td>\n      <td>0.406583</td>\n      <td>-0.055892</td>\n      <td>0.420972</td>\n      <td>-0.219247</td>\n      <td>0.352734</td>\n      <td>-0.379670</td>\n      <td>0.625505</td>\n      <td>0.582764</td>\n      <td>0.289946</td>\n      <td>-0.385064</td>\n      <td>0.455621</td>\n    </tr>\n    <tr>\n      <th>ZN</th>\n      <td>-0.200469</td>\n      <td>1.000000</td>\n      <td>-0.533828</td>\n      <td>-0.042697</td>\n      <td>-0.516604</td>\n      <td>0.311991</td>\n      <td>-0.569537</td>\n      <td>0.664408</td>\n      <td>-0.311948</td>\n      <td>-0.314563</td>\n      <td>-0.391679</td>\n      <td>0.175520</td>\n      <td>-0.412995</td>\n    </tr>\n    <tr>\n      <th>INDUS</th>\n      <td>0.406583</td>\n      <td>-0.533828</td>\n      <td>1.000000</td>\n      <td>0.062938</td>\n      <td>0.763651</td>\n      <td>-0.391676</td>\n      <td>0.644779</td>\n      <td>-0.708027</td>\n      <td>0.595129</td>\n      <td>0.720760</td>\n      <td>0.383248</td>\n      <td>-0.356977</td>\n      <td>0.603800</td>\n    </tr>\n    <tr>\n      <th>CHAS</th>\n      <td>-0.055892</td>\n      <td>-0.042697</td>\n      <td>0.062938</td>\n      <td>1.000000</td>\n      <td>0.091203</td>\n      <td>0.091251</td>\n      <td>0.086518</td>\n      <td>-0.099176</td>\n      <td>-0.007368</td>\n      <td>-0.035587</td>\n      <td>-0.121515</td>\n      <td>0.048788</td>\n      <td>-0.053929</td>\n    </tr>\n    <tr>\n      <th>NOX</th>\n      <td>0.420972</td>\n      <td>-0.516604</td>\n      <td>0.763651</td>\n      <td>0.091203</td>\n      <td>1.000000</td>\n      <td>-0.302188</td>\n      <td>0.731470</td>\n      <td>-0.769230</td>\n      <td>0.611441</td>\n      <td>0.668023</td>\n      <td>0.188933</td>\n      <td>-0.380051</td>\n      <td>0.590879</td>\n    </tr>\n    <tr>\n      <th>RM</th>\n      <td>-0.219247</td>\n      <td>0.311991</td>\n      <td>-0.391676</td>\n      <td>0.091251</td>\n      <td>-0.302188</td>\n      <td>1.000000</td>\n      <td>-0.240265</td>\n      <td>0.205246</td>\n      <td>-0.209847</td>\n      <td>-0.292048</td>\n      <td>-0.355501</td>\n      <td>0.128069</td>\n      <td>-0.613808</td>\n    </tr>\n    <tr>\n      <th>AGE</th>\n      <td>0.352734</td>\n      <td>-0.569537</td>\n      <td>0.644779</td>\n      <td>0.086518</td>\n      <td>0.731470</td>\n      <td>-0.240265</td>\n      <td>1.000000</td>\n      <td>-0.747881</td>\n      <td>0.456022</td>\n      <td>0.506456</td>\n      <td>0.261515</td>\n      <td>-0.273534</td>\n      <td>0.602339</td>\n    </tr>\n    <tr>\n      <th>DIS</th>\n      <td>-0.379670</td>\n      <td>0.664408</td>\n      <td>-0.708027</td>\n      <td>-0.099176</td>\n      <td>-0.769230</td>\n      <td>0.205246</td>\n      <td>-0.747881</td>\n      <td>1.000000</td>\n      <td>-0.494588</td>\n      <td>-0.534432</td>\n      <td>-0.232471</td>\n      <td>0.291512</td>\n      <td>-0.496996</td>\n    </tr>\n    <tr>\n      <th>RAD</th>\n      <td>0.625505</td>\n      <td>-0.311948</td>\n      <td>0.595129</td>\n      <td>-0.007368</td>\n      <td>0.611441</td>\n      <td>-0.209847</td>\n      <td>0.456022</td>\n      <td>-0.494588</td>\n      <td>1.000000</td>\n      <td>0.910228</td>\n      <td>0.464741</td>\n      <td>-0.444413</td>\n      <td>0.488676</td>\n    </tr>\n    <tr>\n      <th>TAX</th>\n      <td>0.582764</td>\n      <td>-0.314563</td>\n      <td>0.720760</td>\n      <td>-0.035587</td>\n      <td>0.668023</td>\n      <td>-0.292048</td>\n      <td>0.506456</td>\n      <td>-0.534432</td>\n      <td>0.910228</td>\n      <td>1.000000</td>\n      <td>0.460853</td>\n      <td>-0.441808</td>\n      <td>0.543993</td>\n    </tr>\n    <tr>\n      <th>PTRATIO</th>\n      <td>0.289946</td>\n      <td>-0.391679</td>\n      <td>0.383248</td>\n      <td>-0.121515</td>\n      <td>0.188933</td>\n      <td>-0.355501</td>\n      <td>0.261515</td>\n      <td>-0.232471</td>\n      <td>0.464741</td>\n      <td>0.460853</td>\n      <td>1.000000</td>\n      <td>-0.177383</td>\n      <td>0.374044</td>\n    </tr>\n    <tr>\n      <th>B</th>\n      <td>-0.385064</td>\n      <td>0.175520</td>\n      <td>-0.356977</td>\n      <td>0.048788</td>\n      <td>-0.380051</td>\n      <td>0.128069</td>\n      <td>-0.273534</td>\n      <td>0.291512</td>\n      <td>-0.444413</td>\n      <td>-0.441808</td>\n      <td>-0.177383</td>\n      <td>1.000000</td>\n      <td>-0.366087</td>\n    </tr>\n    <tr>\n      <th>LSTAT</th>\n      <td>0.455621</td>\n      <td>-0.412995</td>\n      <td>0.603800</td>\n      <td>-0.053929</td>\n      <td>0.590879</td>\n      <td>-0.613808</td>\n      <td>0.602339</td>\n      <td>-0.496996</td>\n      <td>0.488676</td>\n      <td>0.543993</td>\n      <td>0.374044</td>\n      <td>-0.366087</td>\n      <td>1.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "correlation_matrix = X.corr()\n",
    "correlation_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 추신수 jupyter note book에서는 저장된 행렬이나 벡터가 있으면 print를 통해서 뽑기 보다 변수명을 입력하는 것 또는 display()를 통해 보는 것이 가독성 좋게 나옴 **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def visualize_correlation_matrix(data, hurdle = 0.0):\n",
    "    R = np.corrcoef(data, rowvar=0)\n",
    "    R[np.where(np.abs(R)<hurdle)] = 0.0\n",
    "    heatmap = plt.pcolor(R, cmap=mpl.cm.coolwarm, alpha=1)\n",
    "    heatmap.axes.set_frame_on(False) \n",
    "    heatmap.axes.set_yticks(np.arange(R.shape[0]) + 0.5, minor = False) # R.shape[0] 행 수를 제공, minor False를 하면 데이터 이름 제공 아니면 숫자 제공\n",
    "    heatmap.axes.set_xticks(np.arange(R.shape[1]) + 0.5, minor = False) # R.shape[1] 열 수를 제공  minor 뭘뜻할까\n",
    "    heatmap.axes.set_xticklabels(variables, minor=False)\n",
    "    plt.xticks(rotation=90)\n",
    "    heatmap.axes.set_yticklabels(variables, minor=False)\n",
    "    plt.tick_params(axis='both', which='both', bottom='off', top='off', left = 'off', right = 'off') \n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "\n",
    "visualize_correlation_matrix(X, hurdle=0.5) #hurdle 일정 수준이상이 되어야 상관관계 표시 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[6.12684883 1.43327512 1.24261667 0.85757511 0.83481594 0.65740718\n 0.53535609 0.39609731 0.06350926 0.27694333 0.16930298 0.18601437\n 0.22023782]\n[-0.0459523   0.08091897  0.25107654 -0.03592171 -0.04363045 -0.0455671\n  0.03855068  0.01829854  0.63348972 -0.72023345 -0.02339805  0.00446307\n -0.02443168]\n"
    }
   ],
   "source": [
    "corr = np.corrcoef(X, rowvar=0)\n",
    "eigenvalues, eigenvectors = np.linalg.eig(corr) \n",
    "\n",
    "print (eigenvalues)\n",
    "print (eigenvectors[:,8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.linalg.eig` 고유벡터, 고유 값 구하기\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler #sckit-learn 전러치 기능\n",
    "\n",
    "observations = len(dataset)\n",
    "variables = dataset.columns\n",
    "\n",
    "standardization = StandardScaler() # 평균과 표준 편차가 1이 되도록 변환\n",
    "Xst = standardization.fit_transform(X)\n",
    "\n",
    "original_means = standardization.mean_\n",
    "original_stds = standardization.var_**.5\n",
    "\n",
    "Xst = np.column_stack((Xst,np.ones(observations)))\n",
    "y  = dataset['target'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "These are our final standardized coefficients: -0.9281, 1.0816, 0.1409, 0.6817, -2.0567, 2.6742, 0.0195, -3.1040, 2.6622, -2.0768, -2.0606, 0.8493, -3.7436, 22.5328\n"
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def random_w( p ):\n",
    "    return np.array([np.random.normal() for j in range(p)])\n",
    "\n",
    "def hypothesis(X,w):\n",
    "    return np.dot(X,w)\n",
    "\n",
    "def loss(X,w,y):\n",
    "    return hypothesis(X,w) - y\n",
    "\n",
    "def squared_loss(X,w,y):\n",
    "    return loss(X,w,y)**2\n",
    "\n",
    "def gradient(X,w,y):\n",
    "    gradients = list()\n",
    "    n = float(len( y ))\n",
    "    for j in range(len(w)):\n",
    "        gradients.append(np.sum(loss(X,w,y) * X[:,j]) / n)\n",
    "    return gradients\n",
    "\n",
    "def update(X,w,y, alpha=0.01):\n",
    "    return [t - alpha*g for t, g in zip(w, gradient(X,w,y))]\n",
    "\n",
    "def optimize(X,y, alpha=0.01, eta = 10**-12, iterations = 1000):\n",
    "    w = random_w(X.shape[1])\n",
    "    path = list()\n",
    "    for k in range(iterations):\n",
    "        SSL = np.sum(squared_loss(X,w,y))\n",
    "        new_w = update(X,w,y, alpha=alpha)\n",
    "        new_SSL = np.sum(squared_loss(X,new_w,y))\n",
    "        w = new_w\n",
    "        if k>=5 and (new_SSL - SSL <= eta and new_SSL - SSL >= -eta):\n",
    "            path.append(new_SSL)\n",
    "            return w, path\n",
    "        if k % (iterations / 20) == 0:\n",
    "            path.append(new_SSL)\n",
    "    return w, path\n",
    "                                  \n",
    "alpha = 0.02\n",
    "w, path = optimize(Xst, y, alpha, eta = 10**-12, iterations = 20000)\n",
    "print (\"These are our final standardized coefficients: \" + ', '.join(map(lambda x: \"%0.4f\" % x, w)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![비표준화계수](img3/비표준화계수.PNG)  \n",
    "선형회귀분석에서 표준화된 계수 벡터와 편향이 주어지면, 선형회귀 공식을 호출할수 있고 평균 및 표준편차를 사용해 예측 변수를 변환하는 이전 공식은 몇 번의 게산을 거치면 식이 나온다. 이를 파이썬 코드로 다 계산 안하고 구할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "bias:  36.4595\n    CRIM:  -0.1080\n      ZN:   0.0464\n   INDUS:   0.0206\n    CHAS:   2.6867\n     NOX: -17.7666\n      RM:   3.8099\n     AGE:   0.0007\n     DIS:  -1.4756\n     RAD:   0.3060\n     TAX:  -0.0123\n PTRATIO:  -0.9527\n       B:   0.0093\n   LSTAT:  -0.5248\n"
    }
   ],
   "source": [
    "unstandardized_betas = w[:-1] / original_stds\n",
    "unstandardized_bias  = w[-1]-np.sum((original_means / original_stds) * w[:-1])\n",
    "\n",
    "print ('%8s: %8.4f' % ('bias', unstandardized_bias))\n",
    "for beta,varname in zip(unstandardized_betas, variables):\n",
    "    print ('%8s: %8.4f' % (varname, beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figuring out importat features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with standardized coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_regression = linear_model.LinearRegression(normalize=False, fit_intercept=True) # normalize : 0과 1사이의 범위에 있는 모든 변수의 크기를 재조정할지 여부를 나타낸다. x - xmin/ xmax -xmin\n",
    "# Zero score Standardization = x - xmean/ xstd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import make_pipeline\n",
    "standardization = StandardScaler()\n",
    "Stand_coef_linear_reg = make_pipeline(standardization, linear_regression) # make_pipeline = wrapper "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "17.767 NOX\n 3.810 RM\n 2.687 CHAS\n 1.476 DIS\n 0.953 PTRATIO\n 0.525 LSTAT\n 0.306 RAD\n 0.108 CRIM\n 0.046 ZN\n 0.021 INDUS\n 0.012 TAX\n 0.009 B\n 0.001 AGE\n"
    }
   ],
   "source": [
    "linear_regression.fit(X,y)\n",
    "for coef, var in sorted(zip(map(abs,linear_regression.coef_), dataset.columns[:-1]), reverse=True):\n",
    "    print (\"%6.3f %s\" % (coef,var))  # 표준화 이전 상관계수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "3.744 LSTAT\n 3.104 DIS\n 2.674 RM\n 2.662 RAD\n 2.077 TAX\n 2.061 PTRATIO\n 2.057 NOX\n 1.082 ZN\n 0.928 CRIM\n 0.849 B\n 0.682 CHAS\n 0.141 INDUS\n 0.019 AGE\n"
    }
   ],
   "source": [
    "Stand_coef_linear_reg.fit(X,y)\n",
    "for coef, var in \\\n",
    "    sorted(zip(map(abs, Stand_coef_linear_reg.steps[1][1].coef_), \\\n",
    "                    dataset.columns[:-1]), reverse=True):\n",
    "    print(\"%6.3f %s\" % (coef,var)) #표준화 하여 상관계수 측정"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using R squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Baseline R2: 0.741\n"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "linear_regression = linear_model.LinearRegression(normalize=False, fit_intercept=True)\n",
    "\n",
    "def r2_est(X,y):\n",
    "    return r2_score(y,linear_regression.fit(X,y).predict(X))\n",
    "\n",
    "print ('Baseline R2: %0.3f' %  r2_est(X,y)) # R2 값 기록"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.056 LSTAT\n 0.044 RM\n 0.029 DIS\n 0.028 PTRATIO\n 0.011 NOX\n 0.011 RAD\n 0.006 B\n 0.006 ZN\n 0.006 CRIM\n 0.006 TAX\n 0.005 CHAS\n 0.000 INDUS\n 0.000 AGE\n"
    }
   ],
   "source": [
    "r2_impact = list()\n",
    "for j in range(X.shape[1]):\n",
    "    selection = [i for i in range(X.shape[1]) if i!=j]\n",
    "    r2_impact.append(((r2_est(X,y) -r2_est(X.values[:,selection],y)) ,dataset.columns[j])) \n",
    "    \n",
    "for imp, varname in sorted(r2_impact, reverse=True):\n",
    "    print ('%6.3f %s' %  (imp, varname)) # 예측 변수 집합으로 부터 한번에 한개의 변수를 제거하면서 해당 결정 계수를 기록 한 회귀모델을 다시 추정해 기준값에서 뻇다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interaction model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "선형 관계가 좋은 근사 방법이긴 하지만, 흔시 실제 데이터에서 사실이 아닌 단순화한 경우가 있다. 하지만 대부분의 관계는 선형적이지 않으며, 굴곡과 곡선을 보이고 증가와 감소의 변동이 번갈아 나타난다. 예측변수와 응답의 유사성이 높을수록 학습 집합의 적합성이 높아지고 예측오차가 줄어든다.  \n",
    "* 예측변수를 다양한 방법으로 변환해 선형회귀를 개선할 수 있다.\n",
    "* 모든 변환이 잔차오차의 양에 영향을 미치고 궁극적으로 결정계수에 영향을 미치므로, 부분 R^2을 사용해 이런 개선을 측정할 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "비선형성의 첫 번째 원인 중 하나는 예측변수 사이에 발생하는 상호작용 때문이다.  \n",
    "![상호작용](img3/상호작용모델예제_두개예측변수.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위 식처럼 두 개의 예측변수를 가진 모델 예제에서 표현한 것처럼 관계의 추가 정보를 얻기 위해 곱해져야 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.metrics import r2_score\n",
    "linear_regression = linear_model.LinearRegression(normalize=False, fit_intercept=True)\n",
    "create_interactions = PolynomialFeatures(degree=2, interaction_only=True, include_bias=False) # degree 파라미터를 통해 상호작요에 투입할 변수의 수를 정의하며 3개 이상의 변수가 서로 상호작용할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Baseline R2: 0.741\n"
    }
   ],
   "source": [
    "def r2_est(X,y):\n",
    "    return r2_score(y,linear_regression.fit(X,y).predict(X))\n",
    "\n",
    "baseline = r2_est(X,y)\n",
    "print ('Baseline R2: %0.3f' %  baseline)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xi = create_interactions.fit_transform(X) # 새로운 입력 데이터 행렬을 생성하고 원래 데이터에 모든 변수의 상호작용 효과를 부여한다.\n",
    "main_effects = create_interactions.n_input_features_ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Adding interaction     CRIM *    CHAS R2: 0.011\nAdding interaction     CRIM *      RM R2: 0.021\nAdding interaction       ZN *      RM R2: 0.013\nAdding interaction    INDUS *      RM R2: 0.038\nAdding interaction    INDUS *     DIS R2: 0.013\nAdding interaction      NOX *      RM R2: 0.027\nAdding interaction       RM *     AGE R2: 0.024\nAdding interaction       RM *     DIS R2: 0.018\nAdding interaction       RM *     RAD R2: 0.049\nAdding interaction       RM *     TAX R2: 0.054\nAdding interaction       RM * PTRATIO R2: 0.041\nAdding interaction       RM *       B R2: 0.020\nAdding interaction       RM *   LSTAT R2: 0.064\n"
    }
   ],
   "source": [
    "for k,effect in \\\n",
    "    enumerate(create_interactions.powers_[(main_effects):]):\n",
    "    termA, termB = variables[:-1][effect==1] # variables에서 target은 빼야됨\n",
    "    increment = r2_est(Xi[:,list(range(0,main_effects)) \\\n",
    "                + [main_effects+k]],y) - baseline\n",
    "    if increment > 0.01:\n",
    "        print ('Adding interaction %8s *%8s R2: %5.3f' %  (termA, \\\n",
    "                termB, increment))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "R2 of a model with RM*LSTAT interaction: 0.805\n"
    }
   ],
   "source": [
    "Xi = X\n",
    "Xi['interaction'] = X['RM']*X['LSTAT']\n",
    "print ('R2 of a model with RM*LSTAT interaction: %0.3f' %  r2_est(Xi,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "상호작용의 확장  　\n",
    "　  \n",
    "다항식 확장은 원래 변수의 상호작용 및 비선형 거듭제곱 변환을 모두 생성하는 자동적인 수단을 체계적으로 제공한다.　  \n",
    "\n",
    "단순 선형회귀  \n",
    "![단순선형회귀](img3/단순선형회귀.PNG)  \n",
    "2차  \n",
    "![2차](img3/2차.PNG)  \n",
    "3차  \n",
    "![3차](img3/3차.PNG)  \n",
    "다중회귀  \n",
    "![다중회귀](img3/다중회귀.PNG)  \n",
    "　  \n",
    "* 다항식 확장은 예측변수의 수를 빠르게 증가시킨다.  \n",
    "* 더 높은 차수의 다항식은 예측변수의 높은 거듭제곱으로 해석돼 숫자 안정성에 문제가 있으므로 적절한 숫자 형식이 필요하거나 아주 큰 숫자값을 표준화해야 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "linear_regression = linear_model.LinearRegression(normalize=False, fit_intercept=True) # 단순 선형\n",
    "create_cubic = PolynomialFeatures(degree=3, interaction_only=False, include_bias=False) # 3차\n",
    "create_highdegree = PolynomialFeatures(degree=7, interaction_only=False, include_bias=False) # 7차\n",
    "linear_predictor = make_pipeline(linear_regression)  #선형 회귀\n",
    "#quadratic_predictor = make_pipeline(create_quadratic, linear_regression)\n",
    "cubic_predictor = make_pipeline(create_cubic, linear_regression) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "predictor = 'LSTAT'\n",
    "x = dataset['LSTAT'].values.reshape((observations,1))\n",
    "xt = np.arange(0,50,0.1).reshape((500,1))\n",
    "x_range = [dataset[predictor].min(),dataset[predictor].max()]\n",
    "y_range = [dataset['target'].min(),dataset['target'].max()]\n",
    "\n",
    "scatter = dataset.plot(kind='scatter', x=predictor, y='target', xlim=x_range, ylim=y_range)\n",
    "regr_line = scatter.plot(xt, linear_predictor.fit(x,y).predict(xt), '-', color='red', linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "scatter = dataset.plot(kind='scatter', x=predictor, y='target', xlim=x_range, ylim=y_range)\n",
    "regr_line = scatter.plot(xt, cubic_predictor.fit(x,y).predict(xt), '-', color='red', linewidth=2) # 3차 변환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "R2 degree -  1 polynomial :0.544\nR2 degree -  2 polynomial :0.641\nR2 degree -  3 polynomial :0.658\nR2 degree -  5 polynomial :0.682\nR2 degree - 15 polynomial :0.695\n"
    }
   ],
   "source": [
    "for d in [1,2,3,5,15]:\n",
    "    create_poly = PolynomialFeatures(degree=d, interaction_only=False, include_bias=False)\n",
    "    poly = make_pipeline(create_poly, StandardScaler(), linear_regression)\n",
    "    model = poly.fit(x,y)\n",
    "    print (\"R2 degree - %2i polynomial :%0.3f\" %(d,r2_score(y,model.predict(x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "scatter = dataset.plot(kind='scatter', x=predictor, y='target', xlim=x_range, ylim=y_range)\n",
    "regr_line = scatter.plot(xt, model.predict(xt), '-', color='red', linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "scatter = dataset.plot(kind='scatter', x=predictor, y='target',\n",
    "                      xlim=x_range, ylim=y_range)\n",
    "\n",
    "color = iter(['k','g','r','c','m'])\n",
    "\n",
    "for d in [1,2,3,5,15] : \n",
    "    create_poly = PolynomialFeatures(degree=d,\n",
    "                                     interaction_only=False,\n",
    "                                     include_bias=False)\n",
    "    poly = make_pipeline(create_poly, StandardScaler(),\n",
    "                         linear_regression)\n",
    "    model = poly.fit(x,y)\n",
    "    regr_line = scatter.plot(xt,model.predict(xt),\n",
    "                        '-', color=next(color), linewidth=3,\n",
    "                        label='R2 Degree : '+str(d) )\n",
    "    \n",
    "scatter.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "과도한 파라미터화로 인한 성능 저하는 선형회귀 및 기타 많은 머신 러닝 알고리즘의 문제다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overfitting, underfitting 조심  \n",
    "끝\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "R2 of a model with RM*LSTAT interaction: 0.805\n"
    }
   ],
   "source": [
    "Xi = X\n",
    "Xi['interaction'] = X['RM']*X['LSTAT']\n",
    "print ('R2 of a model with RM*LSTAT interaction: %0.3f' %  r2_est(Xi,y))"
   ]
  }
 ]
}